New Models of Galactic Expansion

by Paul Gilster on December 21, 2012

Unexpectedly waking this morning despite Mayan prophecy, I suddenly remembered the storms that had kept me up for an hour during the night. There was little rain, but the winds were gusting and I could hear trees branches slapping against the siding and dogs baying inside nearby houses. When I got up to look out the window, city light under the overcast created a dim bronze aura. You would think it was the end of the world, but this morning I was delighted to see in the paper that a gathering of spiritualists in Mexico says we are not at the end of the world but the beginning of a new one. Up ahead: New powers of telepathy and levitation for us all.

I was never into the Mayan thing enough to know whether it involved the end of just our world or the entire cosmos, but I would guess that any extraterrestrial civilizations, if they’re out there, have likely had their share of doomsday prophets. And as I await my new powers of levitation (not working yet, but maybe by this afternoon), I’m thinking about Fermi’s ‘where are they’ question as we consider our place in the universe. All such speculation plays into so-called ‘percolation theory,’ which was developed to analyze the diffusion of liquids through porous materials, and which can be invoked to study growing civilizations. How do civilizations spread?

Modeling Interstellar Expansion

This is exactly what Thomas Hair and Andrew Hedman (Florida Gulf Coast University) ponder in a new paper modeling the spatial emergence of an interstellar civilization. Percolation theory asks what happens when we pour a liquid onto porous material, tracing its path from hole to hole. But the authors work the question around to this: What happens when a civilization spreads out into the galaxy from a distant star and continues to expand its presence at an ever-increasing rate. Will a colony inevitably get close enough to the Earth that we will be able to notice its presence?

Many explanations for the Fermi paradox exist, but Hair and Hedman want to look at the possibility that starflight is so long and difficult that it takes vast amounts of time (measured in geologic epochs) to colonize on the galactic scale. Given that scenario, large voids within the colonized regions may still persist and remain uninhabited. If the Earth were located inside one of these voids we would not be aware of the extraterrestrial expansion. A second possibility is that starflight is so hard to achieve that other civilizations have simply not had time to reach us despite having, by some calculations, as much as 5 billion years to have done so (the latter figure comes from Charles Lineweaver, and I’ll have more to say about it in a moment).

Image: A detailed view of part of the disc of the spiral galaxy NGC 4565. Have technological civilizations had time enough to spread through an entire galaxy, and if so, would they be detectable? Credit: ESA/NASA.

The authors work with an algorithm that allows modeling of the expansion from the original star, running through iterations that allow emigration patterns to be analyzed in light of these prospects. It turns out that in 250 iterations, covering 250,000 years, a civilization most likely to emigrate will travel about 500 light years, for a rate of expansion that is approximately one-fourth of the maximum travel speed of one percent of the speed of light, the conservative figure chosen for this investigation. A civilization would spread through the galaxy in less than 50 million years.

These are striking numbers. Given five billion years to work with, the first civilization to develop starfaring capabilities could have colonized the Milky Way not one but 100 times. The idea that it takes billions of years to accomplish a galaxy-wide expansion fails the test of this modeling. Moreover, the idea of voids inside colonized space fails to explain the Fermi paradox as well:

…while interior voids exist at lower values of c initially, most large interior voids become colonized after long periods regardless of the cardinal value chosen, leaving behind only relatively small voids. In an examination of several 250 Kyr models with a wide range of parameters, the largest interior void encountered was roughly 30 light years in diameter. Since humans have been broadcasting radio since the early 20th century and actively listening to radio signals from space since 1960 (Time 1960), it is highly unlikely that the Earth is located in a void large enough to remain undiscovered to the present day. It follows that the second explanation of Fermi’s Paradox (Landis 1998) is not supported by the model presented.

There are mitigating factors that can slow down what the authors call the ‘explosively exponential nature’ of expansion, in which a parent colony produces daughter colonies and the daughters continue to do the same ad infinitum. The paper’s model suggests that intense competition for new worlds can spring up in the expanding wavefront of colonization. At the same time, moving into interior voids to fill them with colonies slows the outward expansion. But even models set up to reduce competition between colonies present the same result: Fermi’s lunchtime calculations seem to be valid, and the fact that we do not see evidence of other civilizations suggests that this kind of galactic expansion has not yet taken place.

Temporal Dispersion into the Galaxy

I can’t discuss Hair and Hedman’s work without reference to Hair’s earlier paper on the expansion of extraterrestrial civilizations over time. Tom had sent me this one in 2011 and I worked it into the Centauri Dreams queue before getting sidetracked by preparations for the 100 Year Starship symposium in Orlando. If I had been on the ball, I would have run an analysis of Tom’s paper at the time, but the delay gives me the opportunity to consider the two papers together, which turns out to work because they are a natural fit.

For you can see that Hair’s spatial analysis goes hand in glove with the question of why an extraterrestrial intelligence might avoid making its presence known. Given that models of expansion point to a galaxy that can be colonized many times over before humans ever emerged on our planet, let’s take up a classic answer to the Fermi paradox, that the ‘zoo hypothesis’ is in effect, a policy of non-interference in local affairs for whatever reason. Initially compelling, the idea seems to break down under close examination, given that it only takes one civilization to act contrary to it.

But there is one plausible scenario that allows the zoo hypothesis to work: The influence of a particularly distinguished civilization. Call it the first civilization. What sort of temporal head start would this first civilization have over later arrivals?

Hair uses Monte Carlo simulations, drawing on the work of Charles Lineweaver and the latter’s estimate that planets began forming approximately 9.3 billion years ago. Using Earth as a model and assuming that life emerged here about 600 million years after formation, we get an estimate of 8.7 billion years ago for the appearance of the first life in the Milky Way. Factoring in how long it took for complex land-dwelling organisms to evolve (3.7 billion years), Lineweaver concludes that the conditions necessary to support intelligent life in the universe could have been present for at least 5.0 billion years. At some point in that 5 billion years, if other intelligent species exist, the first civilization arose. Hair’s modeling goes to work on how long this civilization would have had to itself before other intelligence emerged. The question thus has Fermi implications:

…even if this ﬁrst grand civilization is long gone . . . could their initial legacy live on in the form of a passed down tradition? Beyond this, it does not even have to be the ﬁrst civilization, but simply the ﬁrst to spread its doctrine and control over a large volume of the galaxy. If just one civilization gained this hegemony in the distant past, it could form an unbroken chain of taboo against rapacious colonization in favour of non-interference in those civilizations that follow. The uniformity of motive concept previously mentioned would become moot in such a situation.

Thus the Zoo Hypothesis begins to look a bit more plausible if we have each subsequent civilization emerging into a galaxy monitored by a vastly more ancient predecessor who has established the basic rules for interaction between intelligent species. The details of Hair’s modeling are found in the paper, but the conclusions are startling, at least to me:

The time between the emergence of the ﬁrst civilization within the Milky Way and all subsequent civilizations could be enormous. The Monte Carlo data show that even using a crowded galaxy scenario the ﬁrst few inter-arrival times are similar in length to geologic epochs on Earth. Just what could a civilization do with a ten million, one hundred million, or half billion year head start (Kardashev 1964)? If, for example, civilizations uniformly arise within the Galactic Habitable Zone, then on these timescales the ﬁrst civilization would be able to reach the solar system of the second civilization long before it evolved even travelling at a very modest fraction of light speed (Bracewell 1974, 1982; Freitas 1980). What impact would the arrival of the ﬁrst civilization have on the future evolution of the second civilization? Would the second civilization even be allowed to evolve? Attempting to answer these questions leads to one of two basic conclusions, the ﬁrst is that we are alone in the Galaxy and thus no one has passed this way, and the second is that we are not alone in the Galaxy and someone has passed this way and then deliberately left us alone.

The zoo hypothesis indeed. A galactic model of non-interference is a tough sell because of the assumed diversity between cultures emerging on a vast array of worlds over time. But Hair’s ‘modified zoo hypothesis’ has great appeal. It assumes that the oldest civilization in the galaxy has a 100 million year head start, allowing it to become hugely influential in monitoring or perhaps controlling emerging civilizations. We would thus be talking about the possibility of evolving similar cultural standards with regard to contact as civilizations follow the lead of this assumed first intelligence when expanding into the galaxy. It’s an answer to Fermi that holds out hope we are not alone, and I’ll count that as still another encouraging thought on the day the world didn’t end.

The paper just discussed is Hair, “Temporal dispersion of the emergence of intelligence: an inter-arrival time analysis,” International Journal of Astrobiology Vol. 10 Issue 02 (April 2011), pp 131-135 (abstract). The paper on spatial dispersion is Hair and Hedman, “Spatial dispersion of interstellar civilizations: a probabilistic site percolation model in three dimensions,” International Journal of Astrobiology Vol. 12, Issue 01 (January 2013), pp 45-52 (abstract).

I’m not sure that there is currently a similar landmark project in the biological sciences [I’m sure I will get dinged for this; I probably should].

Well, there was the HapMap, the 1000 genomes, and now:

I think the Cancer Genome Project may be closest, but I would view that as far less seminal.

Right.

**This is actually a really important project that could extend millions of lives and save countless dollars in cancer treatment.

As you say.

Also, sequencing of all manner of organisms continues at an ever accelerating pace. Much of this is perhaps not as spectacular as the first human sequence, but every bit as useful, if not more. If space science after Apollo had developed as biology has after the Genome Project, we’d be on Alpha Centauri, now. At least.

But the more important point, science funding has been terribly stagnant since the 90′s boom, and this has in my mind slowed the rate of discovery and discouraged numerous people from continuing in science.

This may be true for other sciences, but as far as I know the NIH budget has mostly been spared so far and likely will be. It can be argued that this is the right way to proceed: Improving our health has the most direct benefit for us, by far, of all scientific endeavors.

Given whatever model of civilization you extrapolate from … what confidence interval do you attribute to your conclusion?
What are error bars , give me a standard deviation.
This whole process involves a prediction interval no way to avoid it.

We do not need a specific model, nor any quantitative predictions. All we need is to convince ourselves that there are some reasonable models that result in colonization. If we can imagine a future for us in which this happens, and convince ourselves that this path we imagine has a non-negligible chance of happening, that is enough. The statistics of large numbers does the rest.

To talk in error bars, if any of your models of “no colonization” has any error bars around zero at all, large or small, then with a large enough number of tries it is nearly certain that colonization will happen. The age and size of the galaxy are such that the number of tries is very large, so your model of “no colonization” will have to have very tight error bars. Do you have such a highly predictive model? Even if you do, can you confidently exclude other models that do predict colonization?

To put the above more succinctly: You are (probably) right that meaningful quantitative predictions about the future of civilizations are impossible. However, this affects the hypothesis of “no colonization” much more severely than that of “colonization”. It is much harder to exclude colonization than to allow it.

“Consider the following hypotheses, one and only one of which must be true:

1) There are no ETI
2) There are ETI but none ever settled down in our vicinity
3) There are ETI around us but we have not detected them”

There Fermi Question is only a talking point , I grant it’s a fun one to talk about but I don’t think that even Fermi labeled it ‘a paradox’, I don’t think he even spoke to the question again.
So the answer would be none of the above or all of the above plus about an aleph-null number of variations on the three statements.
It’s fun to speculate but lack of information makes the ‘question’ and ill posed problem because of the lack of information.

@Rob Henry – why is the age of life on earth a problem? Our galaxy is 13 billion years old, so plenty of time for life to be have seeded from elsewhere by a early technological species..

I don’t assume that life on earth has been interfered/directed since then. Think of the aliens as just wanting to ensure the galaxy is “green”, whatever the diversity of forms produced. For all we know, that is the idea – allow time to create the largest diversity of life forms possible. Possibly meet the technological species that result.

Given that evolution will occur, any race colonizing the galaxy and expecting both biological and cultural evolution to remain static over millions of years seems like hubris to me. Why would they not simply revel in the emergent diversity? Hence why not seed planets with simple life forms and let them develop as they may?

Alex Tolley I assumed that you were trying to alleviate Fermi’s paradox. That can only be done, via the mechanism of panspermia, if life only spontaneously developed once for our galaxy, and its spread thereafter was in such a pattern as to allow the vast majority of ETI to emerge within the same 50 million year period (the time in which galactic colonisation can be completed).

OK, I admit that if we were the product of directed panspermia, that would make our progenitors slightly less interested in suppressing our emergence. Also it would make the zoo hypothesis seem a fair bit more credible but, I think, that is all.

1) There are no ETI
2) There are ETI but none ever settled down in our vicinity
3) There are ETI around us but we have not detected them”

…
So the answer would be none of the above or all of the above plus about an aleph-null number of variations on the three statements.

That is not really a good answer, since I have taken care to formulate the hypotheses such that logically, one and only one must be true. “None of the above” is impossible, because ETI either do or don’t exist, and if they do, they either are or aren’t around us. “All of the above” is likewise impossible, since ETI cannot exist and not exist at the same time. And any variations can still be traced back to one of these three that they are variations of.

Of course, you are free to adjust the definition of ETI if that makes the question easier to answer. In the context of SETI, I suppose ETI would mean any species technologically able to receive or transmit signals over interstellar distances. Likewise, you can adjust the definition of “being around us”, without changing the nature of the question too much.

@Eniac
I have followed the argument about Fermi’s Question for about 50 years , I think on the pages of modern prose science fiction , starting in the 19th century every possible permutation and combination of answers have been explored.
My story is that I first heard the Viewing-Hart-Tipler argument from Tipler myself when he was a post doc at the University of Texas. It was after I had graduated and I was back one year to visit my PhD adviser, he had apparently been arguing with Tipler about the subject, so he showed me to Tipler’s office and left me with him.
Tipler outlined the basic argument, evolutionary biology is a universal model , exclude all the exotic civilizations that are Clarke-ian ‘indistinguishable’, need only one ‘like us’ to arise, the .1c travel speed plus the immense amount of time available and that one ‘typical-human-like’ civilization should be conspicuous by now (I think it was Tipler who thought of von Neuman machines) . Hence there are no XTs. (I have to say Tipler seems to have religious bias about this, I mean real Giordano Bruno – Catholic Church type of thinking, he is a bit of a strange guy).
I felt there was a buried assumption in all this, and I will state it again. I too believe that evolutionary biology can produce a civilization such as us. The flaw that bothers me most is assuming we can predict what our policy for contact will be when we become star faring.
I believe extraterrestrial civilizations exist but I don’t accept the idea that we can predict that they will be conspicuous. We should look for their signature or their signal; we are in real need of empirical evidence, quite different from argument by pure thought. Beyond that , anything that might make us conspicuous to other XT’s when we become star faring can’t be based on our past history or even our present condition.

@ Rob Henry – I see what you are getting at. I am not so interested in whether the galaxy is fully colonized currently, but rather if the galaxy has/had intelligences, or even if it isn’t just sterile apart from Earth. If we assume c is an absolute, then I cannot see a homogenous galactic culture. Indeed I see only limited colonization for almost any reason. But suppose that the galaxy was sterile and life extremely rare, then it might make sense to spread life to these sterile worlds. The costs of spreading life, using ephemeral, replicating machines, might be quite cheap.

I would include widely dispersed life as possible evidence, especially if it appeared that it was more similar than expected.

So Jackson, now I see how your visit to Tipler explains a lot. As you noted, he has a penchant to overextend those sort of hypothesises.

What looks like similar behaviour to my eyes, is your conviction that in the vast diversity of star-travel capable ETI, there is a high likelihood that the fraction complying with the normal (to all biology) Malthusian imperative (wrt galactic colonisation) is infinitesimal.

Two points made by Crick that were telling to me were that life on Earth developed so late that there was easily time and real estate in our galaxy for the same process to have already happen before life begun here. The other is that no matter how far you can travel, you can always send hardy bacteria further. So, could life be seeded here from Andromeda??

Alex Tolley, rereading that old paper of Crick and Orgel, highlights to me was HASN’T happened subsequently to it. In it they made a prediction, the strength of which may not be apparent to those new to the subject, and so I will get to my point circuitously.

The strong correlation between the order of cosmological abundance of reactive elements, and the order of abundance of those most used atoms in biology, has long been noted.
Cosmically H, O, C, Fe, then N
Biologically H, O, C then N with Fe being the most common transition metal used in enzymatic reactions..

Note how extreme this is if by chance from 90 odd choices. Was the universe made to optimise life, or is life more a consequence of what is available? If the latter, then our heavy use of Mo, and light use of Cr and Ni sticks out like a sore thumb just as that paper says.

Now the exiting bit is that it seems that many very early forming stars have an extreme overabundance of Mo, but I could not find a detailed breakdown of these star’s chemical composition. Thus, I have the horrible feeling that Crick and Orgel’s very important prediction that the abundance of trace element usage in biology might match the abundance seen in such stars has not been properly followed up.

This not being my topic, I stand to be enlightened as to that data and its availability, and would be grateful if any here have reference to it.

With all due respect, I still think you are not fully acknowledging the fact that near certainty about the behavior of ETI is only needed to make an argument against colonization. Uncertainty (which I hear you argue exists plenty) leads to a high probability of colonization.

If we assume c is an absolute, then I cannot see a homogenous galactic culture. Indeed I see only limited colonization for almost any reason.

Keep in mind, though, that repeated limited colonization yields complete settlement of the galaxy. Cultural homogeneity is not needed for that. To the contrary, it would be needed to explain a premature end of expansion before the galactic boundaries are reached.

@Rob Henry and Eniac
It was Philip Morrison whose objections to Malthusian growth put me on to it.
I am a physicist and not an evolutionary biologist, but I have tried, in a limited way to study the modern version of evolution as a model for biology. Darwin left some problems in evolution that were not solved until years later. Interestingly these were resolved in mathematics the mathematicians G.H. Hardy and German physician Wilhelm Weinberg who showed that Mendelian inheritance does lead to a maintenance of genetic diversity. This started a whole new era of modeling evolutionary biology mathematically. Ronald Fisher, J.B.S. Haldane , Sewall Wright , Motoo Kimura … and many many other have developed and are still developing mathematical models of evolutionary biology.
Two important things have emerged (among many) to make evolutionary biology work. One is exponential growth messes the process up and needs to be replaced by the Logistic Equation. Secondly to make evolutionary dynamics work parts of the model have to replace deterministic differential equations with stochastic formulations.
Mathematical models of Sociobiology are still in the process of formulation, but just looking at how complicated mathematical biology has gotten I am convinced that Malthusian models fail there too.
Reference:
EVOLUTIONARY DYNAMICS, Martin A. Nowak, Harvard University Press, 2006.

@ Rob Henry – thank you for posting that paper. Given the state of molecular biology knowledge in 1973, that was pretty bold.

It isn’t clear to me why biological use should follow abundance, except for optimizing resource use, as properties are important. For example, even if arsenic was more abundant than phosphorus, could it be used in place of it – I think last years arsenic in Mono Lake organisms controversy would suggest not. Similarly, while silicon is more abundant on earth than carbon, it cannot replace carbon. We don’t even see silicones as inert material used in any organism.

Therefore I tend to think the cosmic abundance argument is really just a coincidence. But as Crick and Orgel state, there just isn’t the evidence to make any predictions.

But I also think we are the cusp of answering this question. Within the next century we will have a good grasp of the space of carbon based life in terms of synthetic biology. We may have samples of life elsewhere in the solar system, and we should have some indication life processes from a number of extra-solar planets.

Where I think we have moved on from the Crick & Orgel paper (apart from our possible origin of life models) is that machines would probably:
1. Manufacture the microorganisms on arrival, rather than store them for the journey.
2. There could be more choices for the underlying biology, which would be based on the properties of the target world, for example, genetic codes that are more robust in high radiation environments.

Someone made the interesting comment upthread that stars will come into close proximity (within a few light years). Are there any stats on the frequency of such encounters over the span of the galaxy’s life? For our sun, how many close encounters would have been experienced since earth formed?

A A Jackson, I suspect the desperation of some to solve Fermi in a SETI friendly way has lead to a failure to carefully segregate cause and effect when evaluating Malthus-like conditions in biology and their subsequent application to galactic colonisation.

In biology when growth is changing from an exponential growth phase to the plateau of a logistic curve, the environment represented by the remaining space and resources becomes incredibly different. In our case an uncolonised star near the end of the process represents prospects almost identical to the same class of star near the very beginning.

Alex Tolley, it seems you understand the topic but not my point. Yes silicon in very common on Earth, and yes the likely explanation for its poor usage in biology is that it is not as innately useful as those other elements. But here we examine the possibility that life here did not start on our planet. Cosmically, silicone is rarer, and carbon much more common than it is on Earth, and the match of availability and usage suddenly becomes startling.

And, yes Crick and Orgel’s expectations were very low (as are mine) but fringe predictions that hold this amount of potential for matching data are rare, and should always be followed up where the work required is minimal.

It isn’t clear to me why biological use should follow abundance, except for optimizing resource use, as properties are important. For example, even if arsenic was more abundant than phosphorus, could it be used in place of it – I think last years arsenic in Mono Lake organisms controversy would suggest not.

I don’t think this controversy shows that at all. There, arsenic was to function in place of phosphorus, within a biochemistry evolved with phosphorus. This is not really expected. In contrast, I believe it is quite clear that arsenic could have very easily taken the place of phosphorus de novo during biogenesis, had it been more common.

Similarly, while silicon is more abundant on earth than carbon, it cannot replace carbon. We don’t even see silicones as inert material used in any organism.

A.A. Jackson: I am not sure I understand how the mathematics of population genetics, your admiration of which I share, is contrary to Malthusian growth. Malthusian growth clearly exists and we see it around us every day. It filled the world with life, it makes an apple rotten, and it kills people with cancer. Or perhaps I misunderstand your use of the term?

As you say, exponential growth turns into a logistic equation, but only in the presence of limits or competition. There are two obvious limits to galactic colonization: 1) the galactic boundary: outwards growth stops when that is reached, and 2) geometry: growth turns cubic when interior colonies have no more neighbors to colonize, and quadratic after the top and bottom of the galactic disk are reached.

Also Jackson, I am mystified as to why so many people try to shoehorn Darwin from the central figure in the history of biology to the central figure in the modern theory of evolution. Just like Winston in Orwell’s 1984, I try so hard to see the party line, but can’t, and, in fact, think that it exasperates the problems you highlighted.

For more than two millennia prior to Darwin, biologists seem to be fairly conflicted as to whether life tends to change into more advanced forms over time or remained static. Unlike of Buffon or Lamarck, Darwin decisively affected this impasse. However I have extreme doubts as to whether his contribution to modern synthesis was comparable to Mendel, nor that it was obviously greater than that of Hugo de Vries. Actually, I find the push to rebrand modern synthesis as neo-Darwinism shocking.

Darwin (like Dawkins) never really seems to have been mathematically minded, and almost certainly did not understand that unless his hypothesis was “that creatures pass on some mutably heritable characteristics with sufficient fidelity that it is possible for enduring advantage to accrue to some lines” then he was building all on an empty tautology. He needed this because he was careful about removing teleology from theory and thence biological thought – and it is for that that he deserves immense credit and fame.

To me Darwin’s theory fell like all the others before the might of the modern synthesis, and it is counterproductive to look back at evolutionary writings before the 1950’s. Now, finally to the point.

Jackson, to me, exponential growth is compatible with evolutionary theory, and it produces what is called stabilising selection. In it we can predict ever faster and simpler replicators, bounded by the verge of the catastrophe error. This is annoying if we wish for great complexity, but great if we wish to remove it (as we do if we are trying to predict the mode of galactic colonisation), it is fantastic!

@ Rob Henry. So let’s go back to my earlier questions. If life reflects the cosmic abundance of elements because this maximizes cosmic resource utilization (rather than local conditions), given samples from different worlds, how could we distinguish directed panspermia from independent geneses?

Alex- modeling the number of close encounters of stars in the galaxy is a complex task. The density of stars increases as you approach the core, but not in a very uniform way. there are stellar number density waves ( the spiral arms) as you move outward. there are open and closed star clusters and the differential speed and eccentricity of star orbits around the galaxy center is unknown. Too close in and encounters are probably common and result in too much planetary bombardment and planetary systems with orbits in frequent disruption. Too far out and the stars themselves are “lonely for visitors” ( like us?) Perhaps most all the ET’s are concentrated in a galaxy ” Commuter Zone” where it is possible to meet other civilizations every million years or so. – and they have little interest in us out here in the backwaters of the galaxy. Why come here where you are stuck for evolutionary time periods without much chance at a cosmic exchange with other ET’s?

@Rob Henry,
I suggest you read the reference I noted:
EVOLUTIONARY DYNAMICS, Martin A. Nowak, Harvard University Press, 2006 for a fuller explanation of how the logistics equations comes into play.

I sure hope you are not questioning modern evolutionary biology.
At this late date it is used with success in all of biology… but especially drug companies who’s researchers use it construct successful pharmaceuticals. If modern evolutionary biology was not true drug companies would not make money off it!

@Eniac
Not accounting for carrying capacity in exponential growth makes successful mathematical models of evolutionary biology crash, see the reference I cited.
The logistic equation may not be the final answer .
It can lead to deterministic chaos which was my fundamental objection to speculation about Fermi’s question.
Even admitting that I think XT civilizations exist.

@Eniac Mea culpa – diatoms are a good example of silicon use. They should also do relatively less poorly compared to calcium shell organisms as the oceans acidify. Grasses also use silica as part of their epidermis. However, the silica is non-reactive and not a replacement for the biochemistry of carbon, which is the main argument regarding life using abundant cosmic elements.

” In contrast, I believe it is quite clear that arsenic could have very easily taken the place of phosphorus de novo during biogenesis, had it been more common.”

I would like to see some basic evidence that this statement is true. AFAIK, it is similar to the “silicon can replace carbon” argument, which is not true (for any conceivable life we can imagine (so far). I don’t know how arsenic could be used as a replacement for phosphorus, but maybe a chemist could explain how this could conceivably work.

A A Jackson, I apologise for not reading reference your before replying , but it turns out to be a book, and thus my reply would be very late. I tried to think of all situations where I can think of offhand where logistics curve came into play in evolutionary theory.

Also, I can’t see how you can read anything that I have written as questioning modern evolutionary theory. I do however question the presentation of the path given to that theory that is commonly outlined in such books, and restate here that such shoehorning of its genesis to where it does not fit creates needless problems of explanation.

Woah, I stop reading this thread for two days and we’re suddenly talking about Orgel and Crick, and I assume we must be talking about the RNA World… which is the most fascinating of all worlds, known or suspected.

Eniac: NIH funding being “spared” is not the same as increasing the budget at a rate that allows continued growth of science. Two key factors: “biomedical science inflation” is often 2-3x normal inflation. A reagent that cost you $50 this year could easily cost $55 within two years and you will also be paying higher salaries for the people in your lab. The stagnant level of funding doesn’t cover the ever larger number of graduating PhDs and postdocs who need to go somewhere. There isn’t enough funding to fully support all of the new labs getting started (and also all of the older established labs). These facts argue that either the current model of science (in the USA—which is BY FAR the best model) needs to be reformatted/tweaked or we need to increase funding at a scheduled, planned rate.

Also, I would suggest that there is a big difference between going to the moon and going to Alpha Centauri. AND, that this difference is substantially greater than sequencing one genome versus 10 or 100 or 1000 or 10000 genomes. Once you sequence the first genome, you can refine the technology to sequence more quickly (there’s a lot more in terms of exploiting chemistry and doing deep sequencing, but once that gate is opened, it stays opened). Don’t get me wrong, there have been a lot of technologies developed in the past decade related to sequencing genomes, and many are revolutionary.

I would compare the Apollo–A.C. difference with something more akin to Dolly the Sheep and actual therapeutic human cloning… Or therapeutic stem cell research; where, a breakthrough in one organism or one application does not necessarily lead to a breakthrough in another organism or a related application because of real differences in molecular biology (don’t ask me for the specifics–I would need to read back over things–, but I know the progress has been slower than expected. Dolly was in 1997).

Regarding ARSENIC: NO, within living organisms on Earth arsenic is not a good substitute for phosphorus. Arsenate (versus phosphate) is far less stable, and thus how would you have a conservation of genetic material. The original paper was bad when it was published, and most people had serious concerns as soon as it was published. There were a lot of chemists very upset since arsenic chemistry had previously been well studied. Additionally, the a number of the controls just didn’t look very good. Basically, you would need to invoke a “molecule X”, which would either stabilize the arsenate or would somehow quickly repair (requiring a lot of energy) damage to the arsenate backbone. The two big concepts for life are: conservation of information and energy expenditures. You must have energy to spend to stay alive and you must successfully maintain enough of your genome to have progeny.

On the whole subject of initiating life… whatever is “simplest” is likely going to be the initiator. So, decide on what you mean by “life” and “simple”, and then think about what would lead to that. I am firmly in the RNA World Hypothesis camp based on our world’s Central Dogma of Molecular Biology [DNA->RNA->Protein]. Simplifying from three biomolecules to one is occasionally contentious, but relatively straight forward based on what we see in today’s organisms. Figuring out how that one biomolecule got started… is rather difficult (impossible without a time machine?) at this point in time, and many people have many different hypotheses supported with data performed in modern labs using “prebiotic conditions”.

@ A.A. jackson“Two important things have emerged (among many) to make evolutionary biology work. One is exponential growth messes the process up and needs to be replaced by the Logistic Equation. “

I have the Nowak book, but I cannot find any reference that pertains to the statement you are making above. The nearest I can come to it is page 13 discussing the parameters to equation 2.8. AFAICS, the issue is mathematical tractability, not the underlying evolution. This is similar to the simplifications economists use to make their models tractable to analysis,

I would like to see some basic evidence that this statement is true. AFAIK, it is similar to the “silicon can replace carbon” argument, which is not true (for any conceivable life we can imagine (so far). I don’t know how arsenic could be used as a replacement for phosphorus, but maybe a chemist could explain how this could conceivably work.

Replaceis maybe the wrong word. Alternative might be better. Arsenic has the same chemical bonding possibilities as phosphorous, and there are numerous organoarsenic compounds to demonstrate that (http://en.wikipedia.org/wiki/Organoarsenic_chemistry). To me, it would be extremely surprising if arsenic were not just as suitable to supplement C-N-O-H as phosphorus is. Maybe structures would have to be a little different, and different enzymes may be needed, but why not?

This is a little more out there, but I even think that biology (not ours, but one just as good) could develop without either phosphorus or arsenic. Life is very adaptable, and in my opinion that goes even for its most basic building blocks. We should not be deceived by the fact that now, after a billion year history, basic biochemistry is written in stone. Just because things are one way now does not mean they couldn’t have turned out very different under different (or even the same) circumstances.

It is kind of like thinking that language has to be written in our familiar 26 letter alphabet. It does not, and there are greek, cyrillic, and pictographical examples to rub our noses in the fact that other alternatives are just as good. In biochemistry we have no such other examples. We have to be careful of the trap of thinking that the way it is is the only way it could be.

Perhaps. But how many, and why have none of them set out to spread their seeds to the galaxy?

I understand you have pondered this question for 50 years, and been present in the original discussions. You have not, however, yet addressed Rob’s and my point: Uncertainty about the future of ETI (and ourselves) favors the colonization scenario. Certainty is needed to exclude it.

Is this wrong? You seem to be making the opposite argument, and I am not able to follow it.

A A Jackson, sorry about the digression, I should start afresh. You gave a reference to a whole book rather than a chapter or page of it. Even if I read the book cover to cover, you couched the perceived problem of logistic growth v exponential in such general terms that I might not recognize your take on it there.

Worse still, I might already understand the problem and solution right now, if you could just explain it in a little greater depth. Anything might do, such as a technical tag they gave the method or the problem it solved.

Alex Tolley, you’re spot on about such a match of element usage having higher potential as an indicator of natural panspermia than its directed counterpart. You might have expected that ETI’s with that technological base would have been able to adjust the trace element usage to their actual target. That work on early high Mo stars should still be done though.

Alex, it also seems that no one has given you a quantitative answer to your stellar close approach question, though jkittle gave a good qualitative one. So I might as well give a rough answer…

If a star stays permanently in a region of identical nature and stellar density to our own, then according to the formula given here from Hipparcos datahttp://www.lpi.usra.edu/meetings/dps97/html/H2501/H2501.html
We should have about 5 encounters within a parsec every million years, and one within .1 parsec (4 light months – if you must) every twenty million.

Alex, if you think that is significant enough to model, then I should go further…

Where we are stars move about 10km/s wrt each other, so every 20 million years they would have moved in the order of a thousand light years. Thus, if we take star-travel to be only practical at < 0.1 parsec, a chronically expansionist ETI starting at our position will undergo exponential growth with a doubling time of 20 million years and we might naively believe that it would take about 20 iterations before backfill slows growth to a logistic curve. In reality they would have neared the galactic bulge about this time and growth should actually accelerate.

Even more sobering, there are only about 200 billion stars in our galaxy, so 37 iterations should do it (¾ of a billion years). It just keeps getting easier!

“Even more sobering, there are only about 200 billion stars in our galaxy, so 37 iterations should do it (¾ of a billion years). It just keeps getting easier!”

I have seen the numbers of stars in the Milky Way galaxy range from 100 billion to 400 billion. So what is the more accurate count? And yes, I do believe it will make a huge difference in all those calculations.

As for life in the Universe, taking into account that we could be seeing all sorts of advanced ETI astroengineering efforts and be totally clueless (or willfully ignorant) about them at this stage in our development, on the grandest scales life does not seem to be a major component of existence. We like to think it is because we are among those little creatures skimming the surface of one small rock, but the Universe seems to be carrying on regardless whether there is only 0ne place with life or gazillions.

Surely the implications of Rob Henrys point (“It just keeps getting easier!”) is that:

1. for any sufficiently long lived civilization of biologicals, star colonization is not going to be blocked by long travel times. Close approaches will allow “star hopping” with relatively modest vehicles.

2. If life can be transmitted by “infected” bodies, then relatively close approaches of planetary systems is going to increase the rate of contamination and thus spread life from system to system. I would like to see the work of the team that looked at this for star nurseries extended.

3. Directed panspermia using replicating machines and biological material could be relatively easy given a sufficiently long time frame, effectively improving the odds of transferring life compared to point 2.

Alex, I am not saying anything about whether or not ETI can spread life among the stars, I am just noting that on cosmic scales it is rather hard to notice. Which seems to imply to me at least that life as we would recognize it is not the fundamental epitomy of the Universe.

Yes, I know about the possibility of stars or even whole galaxies of stars being “alive”, and hey, maybe even Dark Matter is alive, but in this case I am referring to little animacules like us.

Evolutionary time scale being what they are… it is hard to imagine a civilization composed of organisms with our life span staying around for 20 million years. twenty million years ago i believe we were at the lemur stage of evolution. thus I am excited by the implications of star hopping but there are some interesting issues and implications. Unlike much of the discussions on SETI there is some complex but tractable math in figuring out galatic models that predict star encounters.

OK jkittle, good point. It might well be plausible than a species retains chronic expansionist tendencies for a million years, but in twenty million the intelligent species would be an entirely different genus, unless it is stricken by a twenty million year long nostalgia for its original form, or has an inalienable belief in racial purity. Perhaps it does!

It might well be plausible than a species retains chronic expansionist tendencies for a million years

No, this is not plausible. What is plausible is that expansionist tendencies will keep reoccurring, and short of the species dying out, will thus be present forever. And I think we agree that a starfaring species is unlikely to ever die out, never mind how different its forms through the millenia. Millions of millenia, that is ….

It is estimated that the age of half the stars in the Milky Way is about 6.3 billion years. This means that half of whatever intelligent lifeforms there are out there should be 1.5 billion years older than humankind. Considering our own progress in the last 500 years or so, an ET species that began exploring and/or colonizing space 1.5 billion years ago should have been able to map and explore and even colonize the entire galaxy by now, assuming a very modest rate of propulsion capability, like 10% of C. Such a species originating on a planet, say, 1000 lightyears away from us, would need to expand at a rate no faster than 1 lightyear every 1.5 million years, which amounts to a pretty slow sprawl, in order to bump into us. Since science has not detected anyone out there with its very small bag of tools, we have the Fermi Paradox which is largely predicated on the notion that ETis must die out pretty fast (variable “L” of Drake’s equation).

But what if the advanced ETis out there have a hands-off policy with regard to naive, planetbound (and highly aggressive) species like ours? If this were the case, then we would never detect them, even if they were essentially right on top of us. Their stealth technology would allow them to do this if they so desired. Thus the Zoo hypothesis. Or maybe they are quite indifferent to us for other reasons. A cost-benefit analysis of contacting us would make no sense since we are rather far out in the galactic boondocks, and have nothing really to offer them that they don’t already have or that they can’t freely take from us without our knowing (like our music). Add the fact that we are a horrid mess, politically speaking, and you have very good reasons to ignore us.

I guess I forgot to mention something. I do not buy the idea that significant civilizations extinguish themselves quickly, as Drake’s equation assumes. Civilizations that do are not significant, and sure, there will be some that do. But intelligence is not measured by IQ or whatever but rather by the ability to survive in spite of environmental and behavior cicumstances. By this rubric, a species that kills itself cannot be considered either very significant or intelligent, but rather stupid, it seems to me. Intelligence is knowing the importance of expanding its numbers in space, because stars die (or even supernova) and comets will fall, among other things. Expansion is an imperative of biogalactic life. So far we humans must be considered a terrestrial intelligence, not a biogalactic one.

Charter

In Centauri Dreams, Paul Gilster looks at peer-reviewed research on deep space exploration, with an eye toward interstellar possibilities. For the last seven years, this site has coordinated its efforts with the Tau Zero Foundation, and now serves as the Foundation's news forum. In the logo above, the leftmost star is Alpha Centauri, a triple system closer than any other star, and a primary target for early interstellar probes. To its right is Beta Centauri (not a part of the Alpha Centauri system), with Beta, Gamma, Delta and Epsilon Crucis, stars in the Southern Cross, visible at the far right (image: Marco Lorenzi).

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